The homotopy fixed points of Real spin bordism
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917079103307776 |
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| author | Abdallah, Hassan H. Kamel, Yigal |
| author_facet | Abdallah, Hassan H. Kamel, Yigal |
| contents | We show that the 2-local splitting of spin$^c$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_2$-equivariant map in the category of spectra with $C_2$-action from Real spin bordism to a sum of (higher) connective covers of $\mathrm{ku}_{\mathbb{R}}$ and suspensions of mod 2 Eilenberg--Mac Lane spectra. We use this to deduce a corresponding 2-local splitting of the homotopy fixed points of Real spin bordism. We also discuss prospects that arise in the genuine setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10624 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The homotopy fixed points of Real spin bordism Abdallah, Hassan H. Kamel, Yigal Algebraic Topology We show that the 2-local splitting of spin$^c$ bordism by Anderson--Brown--Peterson and Stong refines to a $C_2$-equivariant map in the category of spectra with $C_2$-action from Real spin bordism to a sum of (higher) connective covers of $\mathrm{ku}_{\mathbb{R}}$ and suspensions of mod 2 Eilenberg--Mac Lane spectra. We use this to deduce a corresponding 2-local splitting of the homotopy fixed points of Real spin bordism. We also discuss prospects that arise in the genuine setting. |
| title | The homotopy fixed points of Real spin bordism |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2511.10624 |